There exist jump relation but no poles in the RHP REF . The analysis of the RH problem is based on the so-called Beals-Coifman
operator theory [1]}. Now we use the Beals-Coifman theory to construct the relation between \(m^{mod}\)  and \(\sum _{j=1}^4m^{mod,\xi _j}\) ,
where \(m^{mod,\xi _j}\)  can be constructed by parabolic cylinder equation.
